18
Nonlinear generation of vector beams from AlGaAs nanoantennas Rocio Camacho, Mohsen Rahmani, Sergey Kruk, Lei Wang, Lei Xu, ,Daria Smirnova, Alexander Solntsev, Andrey Miroshnichenko, Hoe Tan, Fouad Kaurota, Shagufta Naureen, Kaushal Vora, Luca Carletti, § Costantino De Angelis, § Chennupati Jagadish, Yuri S. Kivshar, and Dragomir N. Neshev *,Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra ACT 2601, Australia The MOE Key Laboratory of Weak Light Nonlinear Photonics, School of Physics and TEDA Applied Physics Institute, Nankai University, Tianjin 300457, China Department of Electronic Materials Engineering, Research School of Physics and Engineering, The Australian National University, Canberra ACT 2601, Australia §Department of Information Engineering, University of Brescia, Via Branze 38, 25123 Brescia, Italy E-mail: [email protected] Abstract The quest for nanoscale light sources with designer radiation patterns and polar- ization has motivated the development of nanoantennas that interact strongly with the incoming light and are able to transform its frequency, radiation and polarization patterns. Here, we demonstrate dielectric AlGaAs nanoantennas for efficient second harmonic generation, enabling the control of both directionality and polarization of 1

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Page 1: Nonlinear generation of vector beams from AlGaAs nanoantennas

Nonlinear generation of vector beams from

AlGaAs nanoantennas

Rocio Camacho,† Mohsen Rahmani,† Sergey Kruk,† Lei Wang,† Lei Xu,†,‡ Daria

Smirnova,† Alexander Solntsev,† Andrey Miroshnichenko,† Hoe Tan,¶ Fouad

Kaurota,¶ Shagufta Naureen,¶ Kaushal Vora,¶ Luca Carletti,§ Costantino De

Angelis,§ Chennupati Jagadish,¶ Yuri S. Kivshar,† and Dragomir N. Neshev∗,†

†Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian

National University, Canberra ACT 2601, Australia

‡The MOE Key Laboratory of Weak Light Nonlinear Photonics, School of Physics and

TEDA Applied Physics Institute, Nankai University, Tianjin 300457, China

¶Department of Electronic Materials Engineering, Research School of Physics and

Engineering, The Australian National University, Canberra ACT 2601, Australia

§Department of Information Engineering, University of Brescia, Via Branze 38, 25123

Brescia, Italy

E-mail: [email protected]

Abstract

The quest for nanoscale light sources with designer radiation patterns and polar-

ization has motivated the development of nanoantennas that interact strongly with

the incoming light and are able to transform its frequency, radiation and polarization

patterns. Here, we demonstrate dielectric AlGaAs nanoantennas for efficient second

harmonic generation, enabling the control of both directionality and polarization of

1

Page 2: Nonlinear generation of vector beams from AlGaAs nanoantennas

nonlinear emission. We show that the nanodisk AlGaAs antennas can emit second

harmonic in preferential directions and generate complex vector polarization beams,

including beams with radial polarization. This is enabled by specialized III-V semi-

conductor nanofabrication of quality AlGaAs nanostructures embedded in low-index

material, thus allowing for simultaneous forward and backward nonlinear emission.

Our results represent a fundamental step towards efficient nonlinear nanoscale light

sources, finding important applications in bio-photonic imaging and as elements for

efficient nonlinear holograms.

KEYWORDS: nonlinear optics, second harmonic generation, dielectric nanoantennas, nanopho-

tonics, III-V semiconductors, nanofabrication

In recent years, the use of nanoparticles for photon management at the nanoscale has

attracted enormous interest in the scientific community. Enabling new optical functionalities

at the nanoscale requires nanophotonic components capable of manipulating light locally

and then of re-emitting the energy with on-demand frequency, radiation and polarization

patterns.1 We have thus witnessed the development of a plethora of nanoscale metallic and/or

dielectric photonic components, operating as optical nanoantennas for different applications,

including control of light scattering,2–4 and control of quantum emission,5 such as radiation

pattern6 and polarization.7

However, when active control over the radiation frequency is required, new challenges are

to be faced, as this is locked to the emitter’s transitions and cannot be changed by the exci-

tation. While research is underway to overcome this limitation by realising strong coupling

between the emitter and the antenna,8 a lot more flexibility in the frequency conversion can

be realised through nonlinear interactions between the light and the nanoantennas, includ-

ing nonlinear wave-mixing9–11 and harmonic generation.12,13 Indeed, shaping of the nonlin-

ear fields in the harmonic generation process by plasmonic nanoantennas has been recently

tested.14,15 However, the observed efficiency of the nonlinear frequency conversion remains

small, of the order of ∼ 10−11, despite the implementation of different strategies to boost it,

2

Page 3: Nonlinear generation of vector beams from AlGaAs nanoantennas

such as resonant coupling,16–20 three-dimensional geometries,13 or hybrid nanoantennas.21

All-dielectric nanoantennas22 have recently been suggested as an important pathway to

enhance the frequency conversion efficiency beyond what is possible with plasmonics.23,24

The negligible resistive losses of dielectric nanoantennas avoid heating problems and allow

excitation at much higher light intensities, which is of paramount importance for the effi-

ciency of nonlinear optical phenomena.25 Indeed, third-harmonic generation (THG) in Si

and Ge antennas has been recently investigated, showing a huge enhancement of the con-

version efficiency by optically pumping near the antenna’s magnetic dipolar23,26 or anapole

resonances.27 Conversion efficiencies of 10−7 (see Ref.23) and 10−6 (see Ref.27,28) have been

achieved experimentally. These results clearly illustrate the potential of all-dielectric nanopar-

ticles for nonlinear nanophotonic applications.

Despite these spectacular achievements, only χ(3) nonlinear effects have been observed in

these platforms, since Si and Ge do not exhibit bulk quadratic optical nonlinearity, because

of their centro-symmetric crystal structure. However, exploiting materials with second-order

nonlinear susceptibilities, such as GaAs and AlGaAs, would intrinsically increase the conver-

sion efficiency due to the lower-order nonlinearity. The nonlinear effects in GaAs nanostruc-

tures have been the subject of continuing research, including SHG in GaAs nanowires,29–31

hybrid GaAs-plasmonic nanoholes,32 GaAs micro-ring resonators on insulator33 and most

recently dielectric nanoantennas and metasurfaces.24,34–36 SHG efficiencies larger than 10−3

have been theoretically predicted for free standing AlGaAs nanoantennas24 and efficien-

cies exceeding ∼ 10−5 have been recently measured in backward scattering for AlGaAs35

and GaAs36 sitting on an oxide layer. However, no experiments to date have tested the

possibility for shaping the radiation and polarization patterns of SHG, including achieving

unidirectional harmonic generation or nonlinear generation of beams of complex polarization.

Here, we obtain efficient second harmonic generation (SHG) from dielectric AlGaAs

nanoantenna, and demonstrate the possibility of shaping the SH radiation pattern in forward

and backward directions, as well as its polarization state. In particular we prove that the

3

Page 4: Nonlinear generation of vector beams from AlGaAs nanoantennas

SHG emission has a complex spatial distribution of its polarization state, which for a specific

size of the nanoantennas leads to the generation of cylindrical vector beams of radial polar-

ization.37 The properties of our SHG aerials are enabled thanks to a new AlGaAs platform,

which allows for simultaneous forward and backward radiation. Our results demonstrate for

the first time to our knowledge the functional beam and polarization shaping of the nonlin-

ear second harmonic emission from dielectric nanoantennas. This represents a fundamental

step for the manipulation of the angular emission of AlGaAs nanoantennas, which will foster

future studies toward the goal of precision engineering of their nonlinear radiation pattern.

An important strategy to achieve such full control of harmonic radiation is to be able to

fabricate AlGaAs nanoantennas that are accessible from forward and backward directions.

However, the existing fabrication techniques do not allow for this, as they require a non-

transparent III-V handle wafer for direct growth of III-V semiconductors. The growth on

transparent substrates (e.g. glass) is avoided33,35,36 because it results in a high density of

dislocations. Recent works have been devoted to transfer of semiconductor films onto a glass

substrate, followed by the fabrication of micro/nano structures,3,33 however this method does

not allow for fabrication of high resolution nanostructures with smooth surfaces and edges,

which is crucial for the exploration of the bulk SHG from AlGaAs nanoantennas, as our goal.

Here we implemented a novel fabrication procedure of AlGaAs-in-insulator, containing

epitaxial growing technique in conjunction with a bonding procedure to a glass substrate.

Our final sample contains high quality Al0.2Ga0.8As nanodisks partially embedded in trans-

parent Benzocyclobutene (BCB) layer, with equivalent refractive index to glass, on a glass

substrate. Figures 1(a-d) illustrate the fabrication steps (details can be found in Methods).

Electron microscopy images of AlGaAs disks embedded in the BCB and the main sample

can be seen in Figs. 1(e) and 1(f), respectively. Further images on the fabrication steps can

be found in the Supporting Information.

The AlGaAs nanodisks are designed to support Mie-type resonances at both the funda-

mental wave (FW) and the second harmonic (SH). In order to match the excitation of the

4

Page 5: Nonlinear generation of vector beams from AlGaAs nanoantennas

GaAs AlAsAlGaAs

Surface treatment

BCBGlass Substrate

SiO2

500 nm

Peeling off

Sam

ple

Mai

n Su

bstra

te

GaAs

a

b

c d

e

f

Figure 1: Fabrication procedure for AlGaAs nanoresonators in a transparent me-dia. (a) AlGaAs nanodisks defined on a GaAs wafer via electron beam lithography andsequential etching. SiO2 is used as a mask and AlAs as a buffer layer. (b) Formation ofa non-adhesive surface with Cl2 treatment. Sequential removal of the SiO2 mask and AlAsbuffer layer by HF acid. (c) Coating of a BCB layer followed by curing and bonding it to athin glass substrate. (d) Peeling off the AlGaAs nanoresonators embedded into BCB. SEMimages: (e) top-view of the final sample and (f) side view of the main GaAs wafer.

Mie-resonant modes to the FW and SH frequencies, we fabricate nanodisks of various diame-

ters in the range 340−690 nm at a fixed height of 300 nm. Two sets of samples are fabricated:

(i) arrays of nanodisk antennas (1µm periodicity) for linear optical characterization; and

(ii) single nanodisks (5µm apart) for SHG experiments.

First, we measure the linear transmission spectra of the different arrays, Fig. 2(a) (see de-

tails in Methods). The measured spectra are shown in Fig. 2(b). The two vertical dashed lines

indicate the FW and SH wavelengths. We observe a pronounced size-dependant resonance

at the FW wavelength and multiple resonances at the SH wavelength. This is confirmed by

numerical simulations using the rigorous coupled wave analysis (RCWA) method.38 The cal-

culated zero-order forward scattering spectra are depicted in Fig. 2(c). The experimentally

measured spectra are in a good agreement with our numerical calculations.

In Fig. 2(d) we show the extracted scattering cross-section at the FW for nanodisks of

different diameters (see details in Methods). Dots indicate the experimental measurements

5

Page 6: Nonlinear generation of vector beams from AlGaAs nanoantennas

Pu

mp

Sc

att

erin

g,

a.u

.

800 1200 16000

1

2

3

4

5

6

Tra

nsm

issi

on

Wavelength, nm

340 390 440 490 540 590 640 690

800 1200 1600

Experimentb Theoryc

d

N a n o d i s k s’ D i a m e t e r s, n m

ExperimentTheory

300 400 500 600 700

Nanoparticle Diameter, nm

ωω

a

Figure 2: Linear spectroscopy of AlGaAs resonant nanoantennas. (a) Schematic oftransmission measurements of an array of nanodisk antennas. (b and c) Transmission spectraof the nanodisk arrays measured experimentally and calculated theoretically, respectively.Different colors correspond to different diameters of the nanodisks. Dashed lines show thespectral positions of the FW and the SH. (d) Linear scattering of nanodisks of differentdiameters at pump wavelength of 1556 nm. Solid line – theoretical calculations, dots –experimental measurements.

and solid curve the numerical simulations. The resonant profile of the linear scattering,

maximized for disk diameters of 400 − 500 nm, is essentially determined by a magnetic

dipole and a weaker electric dipole excitations in the disk, playing a dominant role at the

pump FW wavelength (1556 nm). Some minor contributions of quadrupoles tend to grow

slightly, when increasing the disk radius. At the SH wavelength (778 nm), higher-order

multipoles are excited in the nanodisks. These two resonant conditions at the FW and the

SH wavelength are responsible for SHG enhancement in our nanoantennas. However, a more

sophisticated dependence of the SHG efficiency on the size of the nanodisk is expected when

taking into account the spatial overlaps of the resonant modes at the FW and the SH fields.

While these results are obtained for arrays of nanodisks, the relatively large period of

1µm assures little influence on the nearest neighbour coupling. Although, some red shift in

6

Page 7: Nonlinear generation of vector beams from AlGaAs nanoantennas

the maximal scattering efficiency can be expected for isolated nanodisks. Therefore, from

these results we can infer the optimal sizes of individual AlGaAs nanodisk to explore for

achieving maximum efficiency of SHG from single nanoantennas.

Next, we use AlGaAs nanoantennas fabricated 5µm apart to be able to detect their

individual nonlinear response, Fig. 3(a). We measure the efficiencies of the SHG in both

forward and backward directions for various sizes of the nanodisks (see details in Methods).

These measurements are only possible due to the transparent and homogeneous surrounding

environment of the AlGaAs nanoantennas enabled by our fabrication. In the experiments

we use linear vertical polarization of pump, which is at 45◦ to the crystalline axes of the

AlGaAs nanodisks in order to maximize the nonlinear tensor component.24,34 The laser beam

of average beam power of ∼ 1 mW is then focused by an infrared objective (NA= 0.85) to

a diffraction limited spot of 2.2µm, resulting in peak intensity of ∼ 7 GW/cm2. Another

visible objective (NA= 0.9) collects the SH from an individual disk in forward direction,

while the focusing objective collects the SH radiation in backward direction. The SH signal

is detected by two cooled CCD cameras, calibrated with a power meter. Further details on

the measurement procedure are given in the Methods section and the experimental setup is

depicted in the Supporting Information. The results of our SHG measurements form a single

AlGaAs nanoantenna of different disk diameters are shown in Fig. 3(b,c). The measured

SH efficiency is shown in Fig. 3(b) and is derived as the sum of the measured forward and

backward SH signals. The overall dependence of the efficiency on the antenna size is complex

due to the large number of higher-order modes existing in the SH frequency band. The most

efficient SHG is observed for the antenna diameter of 490 nm, having conversion efficiency

as high as 0.85× 10−4.

Importantly, as seen in Fig. 3(c), the directionality of the second harmonic emission can

be tailored flexibly by changing the disk size. For example, for disk diameters about 400 nm,

the SH radiation is mostly backward, while for disk diameters 500− 600 nm, the backward

to forward ratio remains close to unity with slight domination of the measured backward SH

7

Page 8: Nonlinear generation of vector beams from AlGaAs nanoantennas

b

300 400 500 600 7000.0

0.2

0.4

0.6

0.8

1.0

-4SH

G E

fc

ien

cy X

10

Nanoparticle Diameter, nm

ForwardBackward

F+B

300 400 500 600 700

1

2

3

4

5

6

Ba

ckw

ard

to

Fo

rwa

rd R

atio

Disk Diameter, nm

2ωa c

ω

Figure 3: Nonlinear spectroscopy of single nanoantennas. (a) Schematic of the singleantenna experiment. (b) Experimentally measured SHG efficiency (PSH/PFW) from a singlenanodisk of different diameter at pump wavelength of 1556 nm. Blue - forward radiation,red - backward radiation. (c) Backward-to-Forward ratio of the SH.

emission. Note that at larger disk diameters, the backward-to-forward ration peaks again,

however, for these larger disks, the dependence becomes very sensitive to the disk diameter

due to the many higher order multipoles that contribute to the SH scattering. The key

feature of our measurements is that we can characterize the nature of the radiation patterns

in both directions, forwards and backwards, as well as in the transverse momentum, as

recently predicted theoretically in Ref.34 Our data, however, suggest that the experimental

measurement apparatus is capturing only a small portion of the total SH radiated power,

due to the finite numerical aperture of our objectives.

To be able to estimate the total efficiency of the radiated SH power, we model numerically

the nonlinear response of the AlGaAs nanodisks with the use of finite element method solver

of COMSOL Multiphysics in the frequency domain. In our simulations, the disk is assumed

to be embedded into a homogeneous medium with a refractive index equivalent to glass

substrate. The material dispersion of AlGaAs is taken from the COMSOL tabulated data.

The second-order nonlinear susceptibility tensor of the [001] grown AlGaAs, possessing a zinc

blende crystalline structure, contains only off-diagonal elements χ(2)ijk with i 6= j 6= k. Thus,

in the principal-axis system of the crystal, the ith component of the nonlinear polarization

at SH frequency is given by

P(2ω)i = ε0χ

(2)ijkE

(ω)j E

(ω)k . (1)

8

Page 9: Nonlinear generation of vector beams from AlGaAs nanoantennas

We assume an undepleted pump approximation and follow the two coupled steps24,26,34,35

to calculate the radiated SH power. First, we simulate the linear scattering at the fundamen-

tal wavelength. To emulate the experimental conditions more accurately, the disk is excited

by a focused monochromatic Gaussian beam, polarized along the [110] direction. The bulk

nonlinear polarization (1) induced inside the particle is then employed as a source for the

next electromagnetic simulation at the doubled frequency, to obtain the generated SH field.

We choose the disk size for maximal SH d = 490 nm and calculate the three-dimensional

SH far-field radiation pattern, as shown in Fig. 4(a). The nonlinear scattering is governed by

the interference of an electric quadrupole and higher-order nonlinearly-generated multipoles

(up to l = 4), leading to the suppression of the forward SH radiation, Fig. 4(a). The side,

top and bottom views of this radiation pattern are also show in Figs. 4(b-d), respectively.

The shaded area in Fig. 4(b) depicts the forward and backward collection angles of the SH

signal in our experiments. These collection angles are also indicated by the inner circles in

the forward and backward far-field radiation images in Figs. 4(c,d). Clearly, the collected

energy in the experiment is less than the generated total SH. By integrating the amount of

the SH emitted within the numerical aperture of the objective lenses used in experiment, we

can determine that only about 30% of the total SH energy can be experimentally collected in

forward and backward directions. As such, the total generation efficiency is estimated to be

three times larger than the measured collection efficiency, thus exceeding the record value of

10−4. This high efficiency provides a solid ground for the use of our nonlinear nanoantennas

as functional elements for nonlinear beam and polarization shaping.

Next, we perform experimental study of the radiation patterns. We build back-focal plane

(BFP) images of the SH radiation pattern by adding a pair of confocal lenses between the

objective lenses and the cameras, in both forward and backward directions. In Figs. 5(a,c

- top row) we visualize portions of the radiation diagram captured by the objective lenses

based on their numerical aperture. From these BFP images we can make the important

conclusion that the SH radiation at normal direction (the (0, 0) point of the BFP images)

9

Page 10: Nonlinear generation of vector beams from AlGaAs nanoantennas

x y

zz

x

NA 0.85

NA 0.9

Top ViewFront View(Forward)

Bottom View(Backward)

min

max

ba с d

NA 0.9

y

0.85

y

x

min

max

pu

mp

NA

1.44 0.9

y

xNA

1.44

Figure 4: (a) Calculated 3D pattern of the Far-field SH radiation. (b) Front view of thepattern. Cones indicate range of angles experimentally accessible with our high-NA objec-tives. (c,d) Top and Bottom view of the radiation pattern (directionality diagrams) of theSH radiation within the experimentally accessible range of angles.

is zero, as recently predicted theoretically.34 Zero SH emission in normal direction here

originates from the symmetry of the nonlinear bulk χ(2) tensor and, thus, is not sensitive to

geometry. As a result, the zero SH emission is observed for all studied AlGaAs nanodisks.

To further support these findings, we also measure THG from the same disks. The third

harmonic relies on χ(3) nonlinear tensor and in contrast to the SH radiation pattern has

radiation maximum in normal directions (see details in the Supporting Information). This is

an important finding when arrays of such SH antennas are considered, as the interference of

the multiple antennas from the array will result in lower efficiency radiation into the zero-th

order SH beam. We also note that surface second-order nonlinearities can in principle result

in normal SH radiation,36 however these are not pronounced in our experiments and the

bulk χ(2) is the dominant nonlinear contribution.

However, what is even more intriguing is the polarization state of the observed far-field

doughnut beam. While most works to date have been focused on the radiation pattern of the

emission, the polarization distribution of the emitted light emitted has never been studied

before. To test the polarization properties of the SH radiation from our nanoantennas, we

perform experimental retrieval of the spatially-resolved polarization states of the BFP im-

ages by using Stokes formalism (see details in Methods). We observe vector-beam formation

10

Page 11: Nonlinear generation of vector beams from AlGaAs nanoantennas

Experiment

Inclination Ellipticity

Experiment

Inclination Ellipticity

Theory

Inclination Ellipticity

Theory

Inclination Ellipticity

a cb d

00.50.85 0.5 0.85 00.50.9 0.5 0.9

00.5

0.8

50.5

0.8

5

Nu

me

rica

l Ap

ertu

re

F o r w a r d B a c k w a r d

00.5

0.9

0.5

0.9

min max min max

Figure 5: Directionality and polarization diagrams of the second harmonic. Toprow: Directionality diagrams in (a,b) forward and (c,d) backward directions. (a,c) Exper-imental measurements, (b,d) theoretical calculations. Arrows visualize polarization states.Bottom row: Experimentally retrieved (a,b) and theoretically calculated (c,d) polarizationinclination angles and ellipticity for the directionality cases of the top row. The incidentbeam polarization is vertical.

at the SH frequency, as shown with the arrows in Fig. 5(a). In particular, in experiment we

observe nearly-perfect radial polarization of the SH in forward direction. In the backward

direction, the polarization state is more complex with polarization inclination having radial

structure and ellipticity ranging from nearly-circular to linear [Fig. 5(c)]. We also calculate

the polarization of the SH beam numerically [see Figs. 5(b,d)]. While the numerical calcula-

tions predict similar polarization states in forward and backward directions, we observe some

differences between theory and experiment. These can be attributed to the slight nonuni-

formity on the surface of AlGaAs as the BCB does not fully cover the nanodisks as well as

due to possible imperfections in nanofabrication.

The nonlinear generation of the vector beams from our AlGaAs nanoantennas can be

intuitively understood by the excitation of Mie-type multipoles at the SH frequency. In

the simplest exemplary case, the vector beam of radial polarization can be emitted by an

electric dipole oriented along the optical axis of the disk antenna. Indeed in our case, higher-

11

Page 12: Nonlinear generation of vector beams from AlGaAs nanoantennas

order multipoles are excited at the SH wavelength. The superposition of these multipolar

contributions is what governs the output polarisation state, which can be highly nontrivial

and can be engineered for a specific application. Indeed, while in forward direction we

observe polarization close to radial polarization state, the backward polarization state is of

a more general nature.

In summary, we have studied the radiation pattern and polarization state of the SH emis-

sion from AlGaAs nanodisk antennas. We have shown that nonlinear conversion efficiencies

exceeding 10−3 can be achieved, so such antennas can be applied for functional nonlinear

devices at the nanoscale. In particular, nonlinear nanoscale light sources of vector beams

with designer polarisation state, e.g. radial polarization have been experimentally demon-

strated, for the first time to our knowledge. Our results open new avenues for novel nonlinear

imaging,39 as well as application as bright fluorescent markers for bio-imaging, as well as for

design of efficient nonlinear holograms.40

Methods.

Sample fabrication: We used metal-organic chemical vapour deposition (MOCVD) to grow

20 nm AlAs and 300 nm AlGaAs (20% Al fraction) on a GaAs wafer. Patterned SiO2 masks

were fabricated on the AlGaAs layer, using conventional e-beam lithography procedure. SiO2

layer was deposited via Plasma-enhanced chemical vapor deposition (PECVD). Then SiO2

disks were transferred to AlGaAs, AlAs and GaAs by reactive ion etching (RIE) technique.

Subsequently, surface treatment has taken place via Cl2 purging by inductively coupled

plasma (ICP) machine, in order to decrease the adhesion between BCB polymer and GaAs

main wafer. SiO2 masks and AlAs layers were removed by hydrofluoric acid, which resulted

in having AlGaAs disks sitting on GaAs wafer with minimum adhesion. The following step

was the spin coating of 4µm BCB layer on the sample, then curing and bonding it to a

thin glass substrate [see Fig. 1(c)]. Finally, the glass substrate with the BCB layer on top,

12

Page 13: Nonlinear generation of vector beams from AlGaAs nanoantennas

containing AlGaAs disks, was peeled-off from the main GaAs wafer.

Optical characterization: The transmission through the AlGaAs nanodisk arrays of size

40 × 40µm and periodicity of 1µm was measured using a home-built optical transmission

system with a white-light source (tungsten halogen light bulb) and a spectrometer (Princeton

Instruments Acton SP 2300 monochromator with Andor DU490A-1.7 InGaAs array detec-

tor). The scattering cross-sections were calculated as ln(1 − T ), where T is the measured

transmission, normalised to substrate.

For the SHG experiments, we place a single nanodisk in a focal spot of two confocal air

objective lenses: Olympus LCPlanNIR (0.85 NA, 100× infrared) for focusing of the FW and

Olympus MPlanFLN (0.9 NA, 100× visible) for collection of the SH. We measure a diameter

of the focused pump laser beam by performing knife-edge experiments, and ensure that the

pump beam is close to a diffraction limit of 2.2µm. The substrate side faces the visible

objective. Thus, the objective lens Olympus MPlanFLN collects the SH from an individual

disk in Forward direction, and the lens Olympus LCPlanNIR collects the SH radiation in

Backward direction. The pump laser is a pulsed Er3+-doped fiber laser (∼ 500 fs, repetition

rate of 5 MHz) operating at a wavelength of 1556 nm. At the laser output we employ a

quarter-wave plate and a half-wave plate to control the output polarization. We use two

cooled CCD cameras to detect the SH radiation. In forward direction a notch filter blocks

the pump laser. In backward direction a dichroic mirror is used in front of the objective lens

to direct the backward SH onto the camera.

Acknowledgements

The authors acknowledge the support by the Australian Research Council and participation

in the Erasmus Mundus NANOPHI project, contract number 2013 5659/002-001. We thank

Igal Brener, Giuseppe Leo, and Isabelle Staude for the useful discussions. The authors

acknowledge the use of the Australian National Fabrication Facility (ANFF), the ACT Node.

13

Page 14: Nonlinear generation of vector beams from AlGaAs nanoantennas

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